Of course that is true, not sure about USA, I don't think there is many state controled companies. Nazis just put that nationalism to another whole level, they didn't put national interest above global in their own country, they also thought that every other nation is inferior and have to be "corrected', that is why they put shame on that word. Today healthy nationalism have to be called patriotism otherwise you get associated with nazis in seconds. But its a word play reallyperhaps so. But if (close to) every nation can be called socialist, then the word does loose its usefulness a bit, doesn’t it? Same with nationalist, for that matter.
And I might perhaps add something: I believe the Nazis were more focused on race than nationality in the stricter sense.
Important part is 'to some degree'. I am ok with some socialistic policies but I don't want socialistic state. Its about balance and prefer more free market than socialistic engineering.